Convergence Analysis of the Spectral Method for Second-Kind Volterra Integral Equations with a Weakly Singular Kernel

Yiao Yong Zhang; Hua Feng Wu

doi:10.4028/www.scientific.net/AMM.263-266.3313

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 263-266Convergence Analysis of the Spectral Method for...

Convergence Analysis of the Spectral Method for Second-Kind Volterra Integral Equations with a Weakly Singular Kernel

Abstract:

The Legendre spectral Galerkin method for Volterra integral equations of the second kind with a weakly singular kernel is proposed in this paper. We provide a rigorous error analysis for the proposed method, which indicates that the numerical errors (in the L2 -norm and the L∞ -norm ) will decay exponentially provided that the source function is sufficiently smooth. Numerical examples are given to illustrate the theoretical results.

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Periodical:

Applied Mechanics and Materials (Volumes 263-266)

Pages:

3313-3316

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.263-266.3313

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Online since:

December 2012

Authors:

Yiao Yong Zhang, Hua Feng Wu

Keywords:

Legendre Spectral Galerkin Method, Volterra Integral Equation, Weakly Singular Kernel

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References

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